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The Grothendieck-Witt group and Voevodsky's slice filtration

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Speaker: 
Marc Levine
Affiliation: 
Essen
Date: 
Thu, 14/07/2011 - 10:30 - 12:00
Location: 
MPIM Lecture Hall

Morel has shown that the 0th homotopy group of the motivic sphere spectrum in the motivic stable homotopy category over a field k is the Grothendieck-Witt group of quadratic forms over k. Voevodsky has defined a motivic version of the classical Postnikov tower, which yields a refined version of Grothendieck's coniveau filtration. We relate these two by showing that the filtration on GW(k) induced by the motivic Postnikov tower is the same as the I-adic filtration, with I the augmentation ideal in GW(k). We examine as well the general question of convergence of the motivic Postnikov tower.

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